If you haven't shredded the chicken yet, you can use two forks and shred it or put it in a stand mixer and use the flat paddle (that looks like a peace sign) to shred the chicken.
In a bowl, combine the Greek yogurt, mayonnaise, soy sauce, sesame oil, and salt & pepper.
In a large bowl, combine chicken, onion, carrot, garlic, and red pepper flakes. Mix well.
Add the sauce to the chicken mixture. Mix well. Taste and add additional salt and pepper. If the salad is too dry, you can add more mayonnaise or greek yogurt 1 tsp at a time.
Serve however you'd like to. Garnish with sliced green onions.
(Optional) you can serve this on Romaine lettuce leaves.
Notes
There are many ways to serve this Asian chicken salad, serving it on romaine leaves is an option. You could also use it in a low-carb wrap.